Following the rise of virtual reality is a demand for sound field reproduction techniques that allow the user to interact and move within acoustic reproductions with six-degrees-of-freedom. To this end, a mixed-source model of near-field and far-field virtual sources has been introduced to improve the performance of sound field translation in binaural reproductions of spatial audio recordings. The previous works, however, expand the sound field in terms of the mixed sources based on sound pressure. In this paper, we develop a new mixed-source expansion based on particle velocity, which contributes to more precise reconstruction of the interaural phase difference and, therefore, contributes to improved human perception of sound localization. We represent particle velocity over space using velocity coefficients in the spherical harmonic domain, and the driving signals of the virtual mixed-sources are estimated by constructing cost functions to optimize the velocity coefficients. Compared to the state-of-the-art method, sound-pressure-based mixed-source expansion, we show through numerical simulations that the proposed particle-velocity-based mixed-source expansion has better reconstruction performance in sparse solutions, allowing for sound field translation with better perceptual immersion over a larger space. Finally, we perceptually validate the proposed method through a Multiple Stimulus with Hidden Reference and Anchor (MUSHRA) experiment for a single source scenario. The experimental results support the better perceptual immersion of the proposed method.
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